Almost convergence and a core theorem for double sequences

The idea of almost convergence was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define the M-core for double sequences and determine those four dimensional matrices which transform every bounded double sequence <f>x=[xjk]</f> into one whose core is a subset of the M-core of <f>x</f>. [Copyright &y& Elsevier]